# How do you find the indicated sum of a geometric series?

Calculate the common ratio of the sequence. This is referred to as r. Your strategy to find r depends on how much you already know about the sequence.
If you know the first and second term, divide the second term by the first term to find the common ratio.

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it might be in any for if it is in a percentage like a is 40 % of b

we know that their ratio will be 4:10

Identify the first term in the sequence. This is referred to as a. You may be able to easily identify this term, but you may need to use other information you have to solve for the term.

If you don’t know the first term in the sequence, but you know the common ratio, the last term and the number of terms in the series you can find the first term by solving for a in the following equation:

last term = a## (common ratio ^ (“n” terms – 1)##)

or

##tn = ar^n – 1 ##

Solve for the sum. The sum is referred to as Sn. Insert your values into the following equation:

sum of series = first term ( 1 – common ratio ^ number of terms) / (1 – common ratio)

or

##S_n=a(1-r^n)÷(1-r)##

hope these answers help you these are not mine if you need any personal assistance u can comment and i will write and other answer

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